A scalable null model for directed graphs matching all degree distributions: In, out, and reciprocal
IEEE Network Science Workshop (2013)
West Point, NY USA
Apr. 29, 2013 to May 1, 2013
Nurcan Durak , Sandia National Laboratories Livermore CA USA
Tamara G. Kolda , Sandia National Laboratories Livermore CA USA
Ali Pinar , Sandia National Laboratories Livermore CA USA
C. Seshadhri , Sandia National Laboratories Livermore CA USA
Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null model to compare algorithms or perform experimental studies. Furthermore, there are scalable algorithms that implement these models and they are invaluable in the study of graphs. However, networks in the real-world are often directed, and have a significant proportion of reciprocal edges. A stronger relation exists between two nodes when they each point to one another (reciprocal edge) as compared to when only one points to the other (one-way edge). Despite their importance, reciprocal edges have been disregarded by most directed graph models. We propose a null model for directed graphs inspired by the Chung-Lu model that matches the in-, out-, and reciprocal-degree distributions of the real graphs. Our algorithm is scalable and requires O(m) random numbers to generate a graph with m edges. We perform a series of experiments on real datasets and compare with existing graph models.
N. Durak, T. G. Kolda, A. Pinar and C. Seshadhri, "A scalable null model for directed graphs matching all degree distributions: In, out, and reciprocal," 2013 IEEE 2nd Network Science Workshop (NSW), West Point, NY, USA, 2013, pp. 23-30.